Abstract
In order to construct efficient public-key encryption scheme that is secure against adaptive chosen-ciphertext attacks (CCA), an efficient signature scheme and an identity-based encryption (IBE) scheme from the learning with errors over rings are presented firstly in this paper, whose security are reducible to the hardness of the shortest vector problem in the worst case on ideal lattices. Secondly, a CCA-secure public key cryptosystem is constructed on the basis of the IBE and signature proposed above. The efficiency analysis indicates the proposed signature and encryption schemes are much more efficient than correlative cryptosystems. The security analysis shows that the IBE scheme is secure against chosen-plaintext attacks, and the public-key encryption scheme is CCA-secure in the random oracle model.
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